GGGGGGOOOOPPPPZPPZwwZwwwww2VVVVVVVttttCCtCCCLLLLLLT))))))))cc===c=====111111=IIII++III++++++++++++;;+;"";"""";;"""_""_______________________~~___~~_~~~_~~~~~~~~~~~~~~~~~~~_~~~~~~~~~~~~~~~~~~~~~~~__~________________________";""";""""";;+;;;+++II+I+II+I=1III
GOGOGGOOOPPPPPZZZwwwwww222VVVVtVVVtCtCCCCLTLLLLLL)))T))))c=cc===c====11111I11I++II+I++;+++;++;;;;;;;;""""""";;""""____________________~___~~~~__~~~~~~~_~~~_~~~~~~~~~~~~~~~~~~:~~~~~~:~~~~~~~~~~~~~~~~~__~_____________________"""";"""""";+;"+++++++++++++IIIII
GGOGGOPPOPPPPZZZZZwwwww22VVVVVVVtttCtCCLLLLLLLTTT)))))cccccc=====111=1111IIIII+II++++++++;;;+;;;;""""""";"__"""______________________~~_~~~~~~_~~~~~~~~~~~:~~::~~~~~:::::::~:::::::~~::::::~~:~~~~~_~~~_~~~_~~_____________________;__";""";;";+;+;+++++++++I+II
OGOOOPPPPPPPZZwwww2w22V2VVVVVtttttCCtCLLLLTLLT)TT))))c=ccc====11=11111IIIII+II++I+++++;++;;;;;;";"""""_"______""__________________~_~~~_~~~~~~~~~~~~~~~::::~:::::::::::~:::::::~~:::::::::::::~~::~~~:~_~~~_~~___~_________________;"_""""""""";;;;+;++++++I+++I
POOOPOOOPPPPZZZwwwww22wVVVVVVVVtCtttCCLLLLLLTTT)))))cccc=cc====1=1=1111I+III+III++++++++;;;;";;;"""""";"__"___""__________________~~~_~~~_~~~~~~~~~~~~~::~::~~:::~:::~:::::::~:::~:::::::~:::~::~~~~~~~~~_~~~_______________________"_"_";"""""";+;++++++I++++II
OOOOPPOPPPZZZZZwwww2V222VVVVttttCttCLLLLLLLTTTT)))T)cccc==c==1=111=1IIII+III+I+++++++++;;;+""";""""""";"________________________~_~~~_~~~~~~~~~:~~:::~:::~:::~:::~:::::::~:::~:::~:::::::::::::::~:::~~~~_~~~~~~~_~______________________""""""""+;;;+;+++++++++
POOPPPPPPZPZwwwwwww2VVVVVVVttttCCtCLLLLLLLTT)TT))))c=ccc====11=1I11IIIII+II+++++++++;;+;";;"""";"""""""______"___________~~~~~_~~_~~~~~~::~~~~:::~:::~::::::::~::~:::::::~:::::::~:::~:::~:::::::~:::~::~~~~~~~~~_~~~___________________"""_";""";;";+;++++++I++
PPPPPPPPZwZwwwwwww2VV22VVVttCtttLCLLLLLLTTT))T))))cc=======11==1=1IIIII++++++++++++;;;;;;;""""";"""___"_________________~~_~~~_~~~~~~~~::~:::::::::::::::::::::::::::~:::::::::::~:::::::::::~:::~:::::::~~~~_~~~~~~~_~_____________________"_"""""""+;;++;++++;
PPPPPPPPPZwwwwwwV2VVVVVVttVttttCLLLLLTLL))T)))))cccc====11=111=IIIII+II++++++++;;;+;"";"";;;""""______"_____________~___~_~~~~_~~~~~:~:::::::::::~:::::::::::::':::':::':::::::::::::::::::::::::~::::::::::~~~~~~~~~~~~___~_________________;"_";"""""";+;;+++;
PPOPZZPZwwwwwwww22V2VVVtttttCCCLLLLLLTTTTTT)))))cccc====11=111IIIIII+II+++++++++;;;""";";;;""____""_________________~___~~_~~~~~~~:::~:::~:::~:::~:::::':::::::':::'':''':'::::':::''::::::'::':::'::~:::::::~~~~~~~~_~~~_~~~_~~________________""""";"""+;";;;"
PPPPPZZwwwwww2w2VVVVVVVtttVtCLLLLLLLLTTT)))))cccccc===1111=1IIII+III++++++++;;+;"""""";"""""____________________~___~~_~~~_~~~~::::::~:::~:::::::::::::''::''::'':''''':':''''''':''':''':':::':':'':::::::::~:~~~~~~_~~~~~~~_~~~_~_________________""""""";";;"
PPPPZwwwwww2V2V2VVVVVVttCttCLLLLLLLT)T))))T)cccc====11=111II+II++III++++++++;;;"""";"""__""___"______________~_~~~_~~~~~~~~:::~::~:::~:::::':::':::':::'::''''''''''''''''''''''''''''''':'''::'':'::::':::::~:::~::~~~~~~~~~~~~~_~~~~_______________"""";"""""_
PZZZZwwwww222VVVVVVVVtCtttCCLLLLLTTT))))))cccc=c==11=1I11I+II+++++++++;;+;;;;"""""""""____________________~~~~~~_~~~~~~~~:::::::::::::::''':''':''':'''''''''^'''^'''^'''^'''^'''^'''^''''''''':''':''':'':::::::::::::~~::~~~~~~~~~~~~__~___~_________"""";""""
PZZwZw2w2wV22VVVVVttttCttCCLLLLLLT)))))))c=ccc===111=1111I++I+++++++++;;;";""""";""""_________________~~_~~~_~~~~~~~~~::::::::::::::::':''''''':''':'^'''^'''^'''^'''^'''''''^'''^'''^'''^'''''''''':'':'':::'::::::::::::~~~~~_~~~~~~~~~~___~__________"_"""_""
ZZwwww2w22VV2VVVVVtttCCCCLLLLLLTL)))))))c==cc====1I1=II1II+II++;+;;++;;;+""";"_"""___________________~~~_~~~_~~~~~::~:::::::::::::':''':''':'''''''''^'''^^''^^'^^''^^'''^'''^'''^'''^^''^'''^'''^'''^'''':'''':':::::::::::::~~~~~~~~~~~~___~____________";""""
Zwwwww2ww2VVVVtVVtCttCCLLLLLLTTTT))))ccc=c=c==1111II=II+I+++++;++;+++;""""_";""""________________~~~_~~~_~~~_~~~~:::~:::~::::::':'':''''''':'^'''^'''^'''^^'^^^^^^^^^^^^^^^'^^^^^^^'^^^^^^^''^'''^'''^''''''''':'':::::::::::::~:::~~~~~~~~__~______________"_""
ZwwwwwV2VVtVVVttVtCtCCLLLLTLL))T)))))c=ccc===111=1IIII+II+++++;++;;";"""""""""___________________~~~_~~~_~~~~:::~:::::::~:::::'':'''''''^''''^'''^'''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''^^'''^'''^''''':''':'':~::::::::::::::~~~~~_~~~_______________"_
wwwww2V2VVtVVtttttCCCLLTLLTT))))T)cccc====11=111=III+I+I+++;++;;;;;;""_";"_"_________________~_~~~~~_~~~~:::~:::::::~:::::':::'::'':'''''^''^^'''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''^'''^''''':''':::::::::::::::::~~~~~~~_~~~__~__________
ww2222VVVVVVttttttCCCLLLLLTTT))))c=cc==c=111=111II++I+++++;++;;;;;""""""_____________________~~~_~~~_~~~~::::::::::::::::''':''''''''^'''^^''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'''^'''^':''':'''::::::::::::~::~_~~~~~~______________
www2V2VVVVVVttttCtCLLLLLLTTT)T))))cccc===1=1===1IIIIIIII+++;;;+;""""""""__;_________________~~_~~~_~~~_~~:::::::::::::::'''''':''''''''''''^^^'^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''^'''''''':::':::':::::::::~:::~~~~~~~~___~___________
22w2VVVVVVtttttttCLLLLLLLTTT)))ccccc=======1IIII+III+++++++++;;"""""""""___________________~~~_~___~~~~~::~:::~:::::::''':::'''''''^'''^'''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'''''''''''':'':::::::::~:::~:~~~~~~~~~~___________
V222VVVVttttttttCLLLLLLL)))))))ccccc===1=1IIIIII++I+++++++++"";""""""""________________~_~_~~~~~~~~~::~:::~:~~~:::::'::'':''':::'''''''^^^^^^^^^^^^^^^^^^^^^^^^^^^^`^^^^^^^^^^^^^^^`^^^`^^^`^^`^^^^^^^^^^^^^^^^^'''^'''''::':::''::::~::::~:~~~~~~~~~~~~________
V2VVVVVVtttttCCCLLLLLTT)))))c)cc=====1===11IIIII++++++++;++;";"";;;"_"""_________________~_~~~~~~~~::~~:::::::~:::~~::::''':''''^''^^'^^^^^^^^^^^^^^^^^``^```^```^`^`^```^```^```^```^```^``^^^`^^^^^^^^^^^^^^^^^^^^''''''''':'':::':::::~:::~~~~~~~~___________
22VVVVVttttttCLLLLLLTTT)))))cccc====11=111II+II+++++++++;"+""";"_"";_""___"__________~_~~~~~~~~~:~::::~:::~:::""";"_";+;"_~:':^':''''''^^^^^^^^^^^^`^^^^^^^``^```^```^```^```^```^```^```^```^^^`^``^^^^^^^^^^^^^^^^^''^'''''':''::'':::::::::::~~~~~_~~~__~____
VVVVttttCtttCCLLLLLL))T)))))cccc===11====1II+I++++++;;+;;;";"";"""__________________~~_~~~~~~~~::::::~~::~"+cwOEW%%@@%%%W4OL;::::'':'^^^^^^^^^^`^^```^```^```^```````^```````````````````^```^```^``^^``^^^^^^^^^^^^^'^^'''''''':::'':'':::::::::~~~~~~~~~~_____
VVVVttttCttCLLLLLT))))))))cc=cc====111=IIIIIII+++;++;";""""""";_"________________~_____~~~~:::~~::~~:~12OB%@##M#MMMMMMMMMMM@BPwwEw=_''^^^^^^^^^`^^```^```````````````````````````````````````````^```^```^``^^^^^^^^^^^^^''^''''':''':'::::::::::~~~~~~~~______~
VVttttttCCLLLLLLTTTT))))cccc====11=11IIIIIII+++++++;"""""";;"""____________________~~~_~~::::~~:::~cE%@####M#MMMMM$MMMMMMMMMM#@@W%%B)~'^^^^^^^```^```````````````````````````````````````````````````````^`^`^^^^^^^^^^^^'^^''''''''':''::'::::::~:~~~~~~~~~~_~~
VtCtttCCCLTLLLTT))))))c)c==c===1=1111I++II+++;;++;";"""";"_"_"________________~~_~~~~~:::::~~:~~:_LB%@@###MMMMMMMMMMMMMMMMMMMM##@@%%w_'^^^^^```^```````````````````````````````````````````````````````^```^``^^^^^^^^^^^^^^^^'''^''''':'''::::::::~::~~~~~_~~~~
ttCtttCCLLLLLT)TTT))))cccc===111=1111I+III++++;;;"""""""""_"_"_______________~~~_~~~~:::::::_~';PW%@##MMMM#MMMMMMMMM$MMMMMMMMMM##@#@%P_'^^^````^```````````````````````````````````````````````````````^```^```^`^^^^^^^^^^^^^'''^^'''':''':'':::::::::~~~~~~~~_
ttCCCCLLLLTTLT))T)c))c=cc===1111=1IIII++I+;+++;;+""""""""__________________~~~~~_~~~~:::::':_LB%#@#MMM#M$##MM#@#M#@MMMMMMMMMMM#M#M@##@B)_^^^```^`````````````````````.```.```.`````````````````````````````````^```^^^^^^^^^^^''^^^'^^''''':''::::::::::::~~~~~_
VCCtCLLLLLTTL)))))c)c==c==1==111=11II++++++;+;;;"""";"_""__________________~~~~~~~~~~:~::~_LB@###M#####M##MMMMMM$MMMMM#MMMMMMMM##@@##@#@BT_'^````````````````.``..```````.`....````````````````````````````````^```^^^^^^^^^^^^^^^^'^''''^':''':'::::::~~::~~~~_
CtCCLLLLLLTTL)))T)cccc=c==1111I1I1IIII++++;++;""""""""_"_______________~_~~~~~~~~:::~::~"C4%####M###M#@#MMMMMM@#MMMMMM##MM##MMMM@%@#@%@%@@%P+^^``````````.``...`..................```.`.`.`````````````````````^```^``^^^^^^^^^^^^^^^^^'^^''''':'':::::::::~::~~
tCLLLLLLLT)T)))))c=ccc===11111111I++II++++;;+"_"""_"_"_________________~_~~~~~~~~:::~__IO%##MM##M#M#M##M$MM##@@#@@#MM#MMMMMM$MMMM###@@@@##@#%V~``````.```......`...``..............`..`...`````````````````````````````^^^^^^^^^^^^^^^^'^^''''':''::'::::::::::~
CLLLLLLLL))T)))))c=cc====11111III++I+++++;";;"_"""""_________________~~~_~~~~~::::::_"TB@@##MMMMM####@@#@##@#MMM$MM##@@###@#MMMMMMMM#@M@#M##@@BL^`````.........`............................`.`````````````````````````^^^^^^^^^^^^^^^^^^^^''^''''':'::~:::::'::
LLLLLLLLT)T)))))cccc=c==111111=1III++++++++;"";""";"__"_____________~~_~~~_~:~~:::~:_=E@@##MMMM#@#MM###@@##M$$$MMM$MMMMMM#M@@@MMMMM$MMM@#####@%D;^`````.```.```.```.```.```.```.``..``.......``.```.`````````````````^`^^^^^^^^^^^^^^^^^^''''''''::'::~::~::::::
LLLLLLLTTTT)))cc=cc====11111111I+III++++;++""";""""______________~__~__~~~~~::::::~"TB####$MMMM#@MMM@###M$$MMM$M$MM#MMM#MM$MMMMMMMMMMMM########@W)^.```````..`.......`.......``.```.```.```.```.`...````````````````````^^^`^^^^^^^^^^^^^^'''''''::''':':::::~::
LLLLTTT)))))))ccccc====111=11III+II+++++;;;""";"_""_____________~~__~~~~~:::::~::~"Z%@###M$MM#MMMMM@@#MM$MM$$MMM#MM#MM$MM##MMM$$$$M$$$$$M$M##M#%%NV:^`````````..`....................``.``..```.`...```````.````````````^^^`^^^^^^^^^^^^^^'^''''''':'::':::::~:~
LLLLLTT))TT)ccccc===1==11111IIII+++++++;;";;""""_______________~~~_~~~_~::::~~~::;P%MMM#MMMM##$MM#MMM$$MM$$MM#####M#MM$MM$$$$$$$$$$$$$$$M$M#@#@%%%BL'````....`....`.`........................``.`.`.```...`.`````````````^^``^^^^^^^^^^^^^^^''''''':'::'::''::::
LLLT))T))))ccccc====11=1=1II+II++++++++;"";""""____________~_~__~~_~~:~:::::::~:_V%#M#MMMM$#@MMM@@MMMM$M###@@@@@@@M#@#MMM$$$$$$$$$$$$$$$$$$MM#@##@%BT^```....................................``.``....`.`....````````````^```^^``^^^^^^^^^^^^^^^'''':'':':::::::
LTTT))))))cc=ccc====11=1I+II+II++++;;;+"";;"_"_______________~~~~~~~~~~:::::::~_LW@###MMMMM#MMM@@M$$M$$M###M##MMM$$$MMMMM$$$$$$$$$$$M$MM$$$$MM#@#@%%D1^``........................................``.```.....```.````````````^^^^`^^^^^^^^^^^^^^^^'''''''':''':::
TT)T)))))ccc=cc=1==111=1IIIIII+++++;";;""";"___"___________~~~_~~~~:::::::~:::~TN##M#M$MM##MM#@#MMMMM####M$MMMM###MM$$$MM$$$$$$$$$MMM###M$$$MMM###@%WP;^```.....................................`.......```...`.`````````````````^`^^^^^^^^^^^^^^^''''''''':::''
)TT)))))cccc=c=1===11IIIIIII++++;;+;"""""";"__"__________~_~~~~~:~~:::::::::::cB@#M#MMMMM#$M@#MMM$$MMM$$MM####MM$$$$$$$$$$$$MMMMM$##@@@#M$$$$$MM#@%%%%P'```.`.........................................`.``..```.`````````````````^`^^^^^^^^^^^^^^^^^'''''''''::'
))))))ccc===c=11=1111I+II++I+++;+;;;""""""_____________~_~~~~~~:::::::::~:'::_w%@###$MMMM#M#M#MM$M##$MMM##@#MMMM$M$$$$M$$$MM###MM###@@#MMMM$M$MM#@%%%%4+````............................................`.``........`.`````````````^```^`^^^^^^^^^^^^^'''^':''''
T)c))ccccc====11=1111I++II++++;++;""""_""_____________~~_~~~_~::~:::::':~:'::LW@###M$MMMM#MMM#MM##MM$M#MM#@#MMMM$$$$$$$$$$$$$$M#M##MMM#MM$M$$$$$M##@%%NDI```...............................................`..``..``...````````^```^```^``^^^^^^^^^^^^^''^''''''
)))))ccccc====11=11I+++II++++++;;""";"__"_____________~~_~~~~~::::::~:''::':=B%@###M$$MMMMMM$MM#MMMMM#@#M#@#MMMM$$$$$$$$$$$$$MM$$MM$MMM$M$$$M$$$MM##%%NNO;^`....................................................`.....`````````````^```^``^^^^^^^^^^^^^'^^^''^''
)))))cccc====1I111II+++I+++++;;;;"""""__"____________~~~_~~~~::::::::::'':'"O%@@##MMMMMMMMMM$MMMM###M#MM$MMM$MMM$$$$$$$$$$$$$$$$$MM$MMM$M$$$MMM$MMMM#%%NN4=^`.........................................................`````````````````^```^^^^^^^^^^^^^^^^'^^''
))ccc==cc=1111111I++++++++;++;;"""""""______________~~~~~~~~~:::::::::':'':L%%%#MMMM$MMMMMMMMM##MMMM$MMM$MMM$MMM$$$$$$$$$$$$$$$$$MM$$MM$$$M$MMM$MMMMM#@%NWBw_`..........................................................`.`````````````````^`^^^^^^^^^^^^^^'^^^'
)c=ccc===111=111II++I+++++;;+;;"""""_______________~_~~~~~~:::::::'::::'''_G%@##MMMMMMMMMMMMMM#MMMMM$MMM@@@#$MMM$$$$$$$$$$$$$$$$$M$$$MM$$$M$MMM$$$M$MM##%NWBG1``.......................................................`..`````````````````^``^^^^^^^^^^^^^'^^^'
c==ccc===111=1IIII++I++++;;;+;""""_______________~_~_~~~~~~:::::::'::''':~L%%@@#MMMMMMMM$MMMMMM#$MMM$M@@MMMM$MMM$$$$$$$$$$$$$$$$$$$$M#MMMM$$$$$$$$MMMM##@%NNBDt:`.........................................................`````````````````^```^`^^^^^^^^^^'^^^'
cccc=c===1===1IIIIII+++++++;;;;"""""________________~~_~~~~:::::::::'':':_Z%%@#MMM$MMMMMMM$MMMMM$M$$M#MM$M$$$M$$$$$$$$$$$$$$$$$$$$$MMMMMMMMM$$$$$$$MMMM#@%%NNBG)^.......................................................`.`.`````````````````^``^^^^^^^^^^^^^'^'
cccc=c==11=111=I+II++++++;+;;";;_"__________________~~_~~~~:::::''::':'::1B%@##MMMMMMMMM$MMMMMMMM$$$MM$$$M$MM#MMM$$$$$$$$$$$$$$$MMM@#@##MM#MMMMMMMMMMM##@@%%NN4EL'....................................................`..``.`````````````````^``^^^^^^^^^^^^^''^
=ccc===111==1III+II++++++++;";;""_______________~~_~~~_~~:::::::::::''::~w%@@#M###MMMMMMMM$#MM$$$$$M$$$$M#M#@#MMMM$$$$$$$$$$$MMMMM%%@N%%@##%#MMMMMMM##@%@%%%%BWB4Z~......................................................`...`.``````````````^```^^^^^^^^^^^^^^^
=ccc===111==1III++II++++;";""";"_____________~__~__~~__~~~~~::::'::':'':+B@@@####MMMMM$$MMMMMM$$MMMM$MMMM@##@@@@%##MMM$M#MMMM#%@##%B%BBBN%%W%@#%@#@@@@#%%%%%%%NWBGL^......................................................`.```.`````````````````^^^`^^^^^^^^^^^
=c=====111I1IIII+I++++++;;;""";"________________~~_~~~~~~~~::::::''''':~2%@@####@MM#MM$MMMMMM$$$MMMMMM##@@@%%%%@%%%#@@#%%@@#@%%@%%BDBBEE4BBGBW%N%%%%%%%%%%%%%%%WN4G=`.....................................................`.``..````````````````^^^^^^^^^^^^^^^^
=c=====1111IIIII++++++;;;;;;"""______________~_~~~__~~~~~~~::::::'''^':ID%@#####MMM##M$MMM#M#$$MMM$M##@@@#%%%%%NWN%NWWWWBB%%%BBNWBOGDGPEGG4PGDBBBWNNN%%%%%%%%%%NNB4Z~.....................................................`.```.```.`````````````^```^^^^^^^^^^^
=====1==111IIIII++++;;+""";;""_____________~~__~~~_~~:~:::~:::::''''^'~TB@@####MM##@#MMMM#$MM$$MMMM###@%@%%%%WBBBNBD44D4DBN%BD4BBDZPGPVPPPEPwOGDDBWBN%%%%%@%%%NNNW4D=........................................................``.`...````````````````^^^^`^^^^^^^
===111=11IIIIIIII++;;;+;"";""_"_____________~~_~~~_~~:~:::::':::''''':"w%@M###MM##@#MM$MMMM#MMMMMM#%%%%%%%%NNBDDB4GDDGEGODBNDOD44D2OP2V2w2P2tPPEE4BWWN%%%%@%%%NNNNB4w:..........................................................`....``````````````^`^``^^^^^^^^
=1111111=IIIII+II+;;+""""""""_____________~~_~~~_~~~~:::::':::'':^^'':+P%@##@#M#@@%#M#MMM#MMMM@MMM%%%N%%%%NWNEG4BGwGGPOPPDBNEPGDDPtOZVt222Z2t2ZEEE4BWW%%%%%%%%NNNWBBO~.........................................................`.......````````````^```^`^^^^^^^
==11=I1I1I++I++++++;+;""""_""__________~_~~~_~~~~~::::::::'':''''''''~1D%@@#@#@@#@@#M#MMM#M#$@#M$#%NBBW%%NWWDZO4GVVP2w22ZDWBwwODEPLP2CLVtVwVCC2PGOEBWN%%%%%@%%NNNBWB4T`.......................................................`...........`````````^```^``````^^
=111=11III++I+;++;;;;"_";""____________~_~~~_~~~~::::::::'''''^''''':_cB@#@@##@@%@####MMM#MMM##MM@%B4BW%NBBGV2DBZLtw2wLCP4WD2VPEP2LP2L)CCC2VCLtwOOODBBN%%%%%%%NNBWNB4Z'........................................................``.`....`..`````````^```^```^^`^^
1111=IIII++II+;++++;""_""_____________~__~~~_~~~~~::::::::''''^'''^':_2N@@@#@@@%@#@@#M#M##MMM@MM#%NDGD4WBBD2CVDOC)VtCC)LZBWGVCZPZwtwCc)LL)tCLTC2ZPZO4BWWNN%%%%NN4B%W4D_................................................................``.`````````````^```^``^^
1111=IIIII+++++;+;;"""_""____________~~~_~~~_~~~~::::::::'''''^'''^':+G%@@@#@#@%@#@#MMMMM#MM#@M#@%WGPEDWBEVLCVDVccVTtTc)PBBPtt2Z2VCwL=)))cLTc)TVZPPPEB4BWN%%%%%%4GW%BBI....................................................................````````````````^```^
=1I1IIIIII+I+++;+;""""_"____________~~~~_~~~_~~:~:::::''::''''^'''^'~cB%#@@#@@%%#@@@#@MMM#M#@@@@%NBPZE4B4PTTLCOT+)V))==cP4GwtTVZVtLw)=)=ccLT=))VPPwZEB44BWN%%%N%BGB%WB)...................................................................`.```````````````^```^
11I11I++I++++++;+;""""""___________~~~~~_~~~~~~:~:::::'':'''''^'''^'"2%@##@@#@%@#@%@M@@###@#@@@%%WDVCGDBEV=))LZc+cc==II1wEGVtct2ZV)t)=c1=cTc=cTCZP2ZEB4G4WN%%%%%WPB%NBt`...................................................................``.`````````````^````
=1I11I++I+++++;;+;""""_""_________~~_~~~_~~~~:::~::::'''''^'''^^''^';ON@@#@#M@@@@@@#@@@###@#@#@%NBGL)PDDZL=cccV=+)1I=I+=ZGGtCcLVwwLt)1cI1cTT=c)CPPw2E44P4WN%%%%%NDW%%Dt`................................................................`..`..`````````````^```^
1111IIII+I+++++;;;;""""_"_"________~~~_~~~_~~:~:~::::::'''''^''^^^''+G%@@###@@#@@@@@%@M#@#@#@##%WBPT=P4D2)==IcV=1)III++cPGEtLcTVwZLTc1c+=TL)1cTTPPwZDBDPBW%%%%%NNB%%%DV^.................................................................``.`````````````````^``
1IIIIIII++++;++;"""""""___"_____~~_~~~_~~~_~:~~:~::::::'''''^^^^^^^:c4@@##M#%@#@@@#@%@MM@#@M@@#%N4C1ItEGtc=1+IC)1c+I;"_IOwZCTc=L2wtT)11I1LT=I=cTPwtPBN4E4NN%%%%NNN%%%BC`.................................................................`...``.`````````````^``
II1IIIII+++++++""""""""___"_____~~_~~~_~~~~:::~::::::'''''''^^^^^^^_VW#@##M@@#@@%@#%%@M#%@@#@@#%WZ)I+L4ZT=II"Ic)=c"I+_"IPtZCT=1=2Pt)cI+1ILL=I=)wwVwDBBDG4NN%%%%NN%%%%BT`..................................................................`...`.`````````````^^`
IIIIIIII++++;;;""";"___________~~~~~~~_~~:~:::~:::::''''^'^^^^^^^^^_Z%M###@#@@@@%#@%%#M@@@@M%%#%Dt=+;=DVcI+"_~ITI+I++"_1ZVwC=c+1VOVc11""I)L===CLVPGD4GGDBW%%N%%N%%%%%B1..................................................................``.....`````````````^``
IIII+II++++;;;;""";"____________~~~~~~~~::~::~~:::::''''''^^^^^^^^^;G%###@####@%@#@%%##@@#@#@%%NPt=+;1OL+I;::~_=;++I"__)VcCL+=;"1twt;_;__;cLIc)CV2OOPPD4D4%%N%%%%@%%%4"...................................................................`.```.`````````````^``
IIII+I++++++;;;""";"___________~~~_~~~~::::~::::::::''''^'^^^^^^^^'+D%MM#####@%@@#%%@#@@@@M@%%%WOL=;_cET;_:^`'^I=+;__:_I=;_)+++~:"LLI__:__;1L2OOED4D444OO4N%%%%%%%%%%D:...................................................................`.`...````````````````
IIII+II+;++;""""";""___________~~~_~~~~:::::::::'::'''''^^^^^^^^^^'1B@MM##MM@@@#@@%@##%%@#M%BN%WGL1;")L+_':_"__1V==_::~~'~'":~":^^~+__~"I)2PZOZVL)==1TZGGDN%%%%%%%#%NZ'.....................................................................``..`.`.````````````
I++II++;+;;;"""";"____________~~_~~~~:::::::::'':'''''^'^^^^^^^^^^^cW@MM##M#@@@#@%%%M@%%@##NBNNBGT+""=;;+I=)LTTVPw2c1;~'''`:'^:'``^:~~"cLwZZVVc;___"_+TVwG%@%%%%%%#@WV^.........................................................................`.``````````````
II+++++++;;"";""""_"__________~~_~~~~:::::::::'':'''''^^^^^^^^^^^^^L%###MMM#M@@@%%%%M%%%@%#WB%N4P)+__c)=+_:_;++TVwCLt)c+_`..`......``'+cLLL=;~'''':__"1TVG@#@%%%@%@@BV^.........................................................................`..`````````````
I+++++;;+;_;""""_____________~~~_~~:~:::::::::':'''''^^^^^^^^^^^^^'w%###$MM#@#@%%%%@%%%%%@#BBNWPZT_++_^`....`..^~"+1cI+"~'....  . .`^'~""_______:::~~_I)LZ%#@%%@@@#@WV`... ... . ...............................................................`.`...``````````
++++++;++;""""_"_____________~~~~~~:::::~:::::''''^''^^^^^^^^^^^^^~Z%##M$MM@M#@%%%%@N%%%%#%D4W4VV1~:^`.....`^^^'::'^''^^``...     ..^':~_~___I1==1+___+1c2%@@@@@@@@@B2^..      .  .............................................................``..`..``````````
++;+++;;;"_"""_____________~_~~~~~:::::::::::'''''^'^^^^^^^^^^^`^^"D@#MM$M#@M@@%%%@%%%%N%@WDEBPT+:^^^`.```^^~______~^`^``..      ..`^':''_c2OOOD4Ot1""++=CW@@@@###%@BV^..  .   .  .............................................................``.....``````````
++;++;;;;;"";"____________~~_~~~~~::::::::'':'''''^''^^^^^^^^^``^'=B@#MMM##MM@%%%%%N%%N%#%4PGDt+~'^^^^`^^;LPGOODDw)"_'`^.`...   ...^:'^:"VBBGNt^_VDOc"""+TB#@%@@@##%BV'.    . ..  .....................................................................`````````
+++++;;""""";"____________~~_~~~~::::::::''':'^'''^'^^^^^^^`^``^^'TN@MMMMMMMM@%%%@%N%%N%@WO2PP1~^^^^'''_)GOtBNOGBL)LI~^^^`..    .`^::^'_1PODDPO:'1tVc__~"=D#@@###@@%42'.    ..     . ...........................................................`.....``````````
++;++;";;""""_____________~~_~~~~::::::::'''''^'''^^^^^^^^``^^`^^'2%#MMMMMMMM@%%@%N%%N%@%4wVEt~'^``^''~=ZV_IDPPZEI.^cI''`^`..  ..`^~^^:='~PwVD=.~TPV+~:__IO##@###@@N4O:.           .  ..  ............................................................``````````
+++++;;""";"_"___________~~~~~_~::::::::'':'''''^''^^^^^^^^`^^^``:P%#MMMM$$MM@@@#%%%%N%@NGVZO=_^^```^'_=V2)IwDVZG:..+)~^`^`......`':'^_T+~TEGP_^=tt)"~::_1Z%##@##@@WDP'  .   .   . ...............................................................`.```.````````
++++;;;"";;"____________~__~~~_~::~::::::':'''''^''^^^^^^^^^`^^``_G%#MMMM$$M@#@%%%%%%%M%BPVV=_'^```..^~+IcLTcVPV1"Icc)=^^^``.....`'''`'_~_____I1"___~:::~;V%##@@##@B4P'. .   .        .  . .........................................................`.`.````````
++++;;;""";"_""____________~~~~~::~::::''':'''''^'^^^^^^^`^^``^``_D%MM$MM$$M##%%@%%%W%M%EVL=_:'^`....`^^'~~:':''~::'''^```^`....`^''^`..`^^`^^^`^'':''''~"T%@#@@##%BDP: ..       .   .   ... . ......................................................``..```````
++++;;;""";"__"__________~_~~~~~:::::::::'''''''^^^^^^^^^`^```^``"B%@MMMM$$MM@%@%%%NB%M%OC=;~:'^`.....```^^`````^'^'^^...````...`^'^^^....`.````^^^^`^^^~")N@@@@@#%4DP: ..       .       . ..........................................................`...```````
;+;"""""""""_____________~_~~~~~::~::::'''''''''^^^^^^^^^`^```^``+B%@MMMM$$$M@M%%%%NBB#%PLI"~:^^```......``...```^^`.....`^``...`^'^`^`.........`.```^^'~")N#@@@@@%BDP:...   .   .       .   .. ....................................................`.`...`.````
;;+;";"""";__________~___~_~~~~:::::'::''''''''^^^^^^^^^``^```^``+B@@MMMMM$M@#@%@%%4DB%%GL="~:'^```......................```^`.`^^'^```.............``^:~")N#@@%@%%BDP: ..   .   .          ..  ......................................................`.````````
;++;"""""""____________~~~~~~~::::::::::'''''''^^^^^^^^^^^^```^``IB%##MM$M$M##@@@%%BGDN%Dtc;~:'^``...... ..........   ....```...^^'^^^`..............^^:~"L%#@#@%@%B4P:  .   .   .   .   .   .  .....................................................``.````````
+;""""""""___________~~~_~~~~:::::::::''''^'''^^^^^^^^``^```^````IB%##MM$MMMM%@@%N%NDEB%4Vc;_~^`^`......    .  ..     ....`^^...^^''^^``.....  ......`^:~_C%#@##%%%B4P:.                   .  .. .........................................................``````
+""""""";____________~~~_~~:~:::~::':'''''^''^^^^^^^^^``^````````1B%@#MMMMMM###@%NDPZPDN42)+_~'^^`....                ....`^^...^'::^^^`. .    .  ...`^:__2####@%%%WBP~.                         ... .......................................................````
+""""""""____________~~~_~~~::::~:'':'''''^'^^^^^^^^^^``^````````IB%@#MMMMM###@@%%OttwOWBVc1_~'^^^`...               ....`^^^. .^':~:^^`.. .   .. ...^^:_"P#@##@%%%WBP~.                       .   . ......................................................`````
;""""""""__________~_~~~_~~~~::::::::'''''^'^^^^^^^^^^``^````````IB%###MMMM#M##@#MM#M#@N4VT1"~'^^^`...              ....`^^''...^'~_~:'^..         ..^':_IB###@@%%%WBZ:.   .                       . ...................................................`..``.``
"""";"__"__________~_~~~_~~:::::~:'':'''''^^^^^^^^^^^```^````````+B%@##MMMMMM###$MMM$MM@Dt)=;_:^^^`...              ...`^:''^...^'____:^`. .      ...`'~_L%@##@@%%%WBP_.                           .....................................................`...`.``
;""";"__;"________~~_~~~_~~:~:::::'::'^'''^^^^^^^^^^^```^````````;4%%##MMMMMM##M$$$M$MM@DVc=+_:'^^``..             ...`':::'^` .`^~____:`...      ...`'_;O@###@@%%%NBE"..                             .................................................`....`.``
;""";"_"__________~~~~~~_~~:::::::''''''''^^^^^^^^^`^```^````````;B%%##MMM#MMM#M$M$$$$M#Dtc1I_:''^``..          ....`^:_~~:'^.. .`'_"___^...      ...`'_)N@@#@@@%%%WBO+..                             ....................................................`...``
"""";"____________~~_~~~~~::~:::~:'':'''''^^^^^^^^^`^```````````^+B%@#MMMMMMM#MM$M$$$$$MBtcI+_::'^^``..        ..`..`:~~~::^`.  ..^~____^....  .  ..`^:_w%MM##@%%%NWBDc..                             ..................................................`.`.`.``
"";""""___"______~_~~~~~~~~:::~::::''''''''^^^^^^^^^`^^``````````+W%%#MMMM$MMMMMM$$$$$$MBt)1;"_:^'^^`..       ...``.`:~:':_'`..  .`'~___^`..... ....^'_;G##@@#@%%@NBB4T...           .   .   .   .   ...................................................```.````
";;"_""_________~~_~~~~~~~~:::~::::'''''^^^^^^^^^^^^^`^^`````````IW%%#MMMMMMMMMMM$$$$$$MNV)I;__:'''^`...     ..```...''^^^'`..   .`^:~:'^^`........`^~_cW##@###%%%NWBBV^..           .   .   .   .   ...................................................```.````
"";;"___________~~_~~~~~~:~~:::::':'''''''^^^^^^^^^^``^``````````=W%%#MMM#MMMM#MM$$$$$$M%w)1;_~:'''^`........`^`.....`''^^^^`.   ..^:~:^^^`^^``.``^^:_;V@M#@#M#%%%NWWBP".            .   .   .   .   ................................................`..```.```.
""""__"_________~~_~~~~~~~~~::::'':'''''^^^^^^^^^`^```^``````````)N%%#MMM#MMM##MMM$$$$$MMP)1;_~:'''^^``.....`^^......`^^'_~:'`....^:_"~^^^^^^^^^^^^:__1B#M#@#@@%%%NWNWE=`.           .   .   .   .   ...................................................```.```.
""""____________~~_~~~~~::~::~~::':'''''^^^^^^^^^^^``````````````TW%%#MM#######MMM$$$$$$MDTI;_~:''^^^^``..``'^`.......``^^^':'^^`^:~~~'^'^^^''^^^^'~__C@#MM##M@%%%N%%W4t'.               .   .   .   .................................................`.```.```.
""""__"_________~~_~~~~~:~~~:::::':'''''^^^^^^^^`^^`````````````^CB%%#MM##@MM###MM$$$$$$$%C=+__'''^^^^^``.``^.````.....```````^``^^'':'^'^'::'^^^':__;D##M#@##@%%%%%%NBP_.           .   .   .   .   ...................................................```.```.
""______________~~_~~~~:::~:::::'':'''''^^^^^^^^`^^`````````````^CB%@#M#########MMM$$$$$$#G=+"_:''^^^```..`^.`''^^``.````^````^```^^'''':~_~:'^`^'~__C@#MMM@#%%%%%%%%%BGI.               .   .   .   . .................................................``..```.
"______________~_~~~~~::~:::~:'::'''''^''^^^^^^`^^``````````````^CB%@@##@#@#####M#@M$MM$$MBc+"_::^^^^``....`.`:~_'^^``.````^^'^^^^^''':::_;~'^`^^'__;OMM###@#%%%%%%@%NBGI.                             .........................................................
"______________~_~~~_~::::::::'::'''''^'^^^^^^^`^```^```````````:tB%@#####@@####MM@M$MM$$$MP1+_~:'^^^^`.....``^IEL__"_~''`...```^^^':~__1=~'^``^^:__C##M##@#@%%%%%@@%WBGc..                            . .......................................................
"______________~_~~~_~::::::~:'::'''''^^^^^^^^^^^```````````````:2B%%#M###@@#####M@M$MMM$$M%CI"_~:''^^```....``:CP)I..'~:~::'^^'_:_"_IV2)~'^```^:~_1B#MM#%@@@%%%%%@#%NBBt'.                            .........................................................
"____________~~~~~~~~~::::::::'::''''^^^^^^^^^`^^```^```````````~LB%%@#####@#@@#MM@#$MMM$$MM%L+;_:''^^```...`.``^+LV1:'.....^:':^^._TVC=_'^^^^^'~_+B##MM##@@#@@%@%##@NBB2_.                            .........................................................
"_____________~~~~~~~::::::::''::''''^^^^^^^^^`^^```````````````:cB%@@#M###@@@@#M#@#$MMM$$$M#Gc+"_~:'^^^``......`^'_+)T)+:..^~''_"+Tc=I"'^^'^^:__"OMMMMM#%@@#@#@%%@@%%WBV;.                            .........................................................
""___________~~~~~~~~::::::::'':''^'''^^^^^^^^``^```^```````````~)4%%@@M###%%@@@MM@#$M$M$M$M%DwTI"_~:'^^^`````....`'~__"";+II+++;"_";+"~'^^^^'~_"Z#MMMMM#%#M#%#@NN#%%%W4wI.                            .........................................................
_____________~~~~~~~~:::::::::''''''''^^^^^^^^``^```````````````:1DN%@#M#@@#@@@@@M@@MM$M$M$M%EZ2L1"_~:''^^^`^`.....`':''^`...`.`^^'_;_:'^^^''^~_ZM#$MMMM#@#M###%WB@@%WNBOI.                              .......................................................
_____________~~~~~~~~:::~::::''':''^'^^^^^^^^^^`^```^```````````'+EN%@#MM@@@@@@@#M##MM$M$MMMNG2VtT=;__::'^^^^`..`..``^:::^....`^'':_:'^^^^'':_;Z##$$M$MM###M##@%BGW%%NWWOc`                            .........................................................
_____________~_~~~~~::~:~:::::::''''^''^^^^^^^^^`^^`````````````^;O%%#MMM@@@@####MM#M$$$$$$MWEZ2tLLI__~:'''^^``.`..```^':'^..`^'::::''^^^^'':_c%MMMMM$MM#M####@W4EW%%%NBGT`          .   .   .   .   . .....................................................```.
_____________~__~~~~::~::::::'::'''''''^^^^^^^^^``^`^```````````'"Z%%@#MM#@@@#M##MM##M$$$$$#WEZ2tLLT=+_~:::'^^^`..`..``^^^^'^'''^'^^^^^^^'::_=N#M$M$$$MM####@@%%WEB%%%NBO=.          .   .   .   .   . ...............................................`...`.```.
_______________~~~~:::~::::::::''''''^^^^^^^^^^^^^^`````````````^_2N%@#MMM@#%##MMMM##M$$$$$#WEP2CLL))cI;__~'^^^`..`.......```^^^```````^':~_L#M#M$$$$$MM###@@@%%%WWNN%NBGc.          .       .   .   . ..................................................``.```.
____________~~_~~~~:::~:~:~:::'''''''''^^^^^^^^``^^``````````````~CW%%@MMM#@@@#MMMM##M$$$$$#WDP2CLL)ccc=+"_:'^^`^`..................``^^':_t%@#MM$$M$MM@@#@%%WN@%NNWN%NBG=.          .       .   .   .   ................................................`..```.
_____________~_~~~~:::~:::::'::'''''^^^^^^^^^`^^`^^``````````````'TB%%@MMMM@@@#MMMMM#M$$$$$#BDP2CLL)cccc=1+"_:'^^``....      ........^^^:_VN%BW#$$MMMM#@@@@%%BBN@@%%%NNBP+.          .       .   .   .  .................................................``.```.
___________~_~_~~~~:::~~::::'::''''''^^^^^^^^`^``^^``````````````^=B%%@#M$$#@#@#MMMM#M$$$$$%W4O2VLL)c===1III__~:'^``.....       ....`^''_tGDBNDG4N####@%@@%%@WB4%#%%%%WBG;.          .       .   .   . . ...................................................```.
___________~~~_~~~~:::~__:::::''''''^^^^^^^^^`^^`^^^``````````````"D%%@#M$$M##@@MMMMMM$$$MM%B4OwVCL)==111II;"""_:'^^`......     ...`^'';t2wPE4D2wPD%@%%%%%%##@BDB@###%%BZ:.          .   .   .   .   .   ................................................``.```.
___________~_~~~_~~:~::~~:':::''''^''^^^^^^^^^``^```^`````````````_G%%%#MM$M#@@@#MMMM#M$$M#NB4OwVLT)c1II1I+;"____:^^^`..`.........`^^'_T2V2ZOEDZL2G%%%%%%W%##%BGB%###%%W2^                             .   .....................................................
___________~_~~~_~::~:::~:'::'''''^''^^^^^^^^^``^````````````````^"G%%%@MM$MM#@#@#MMMMM$$M%NB4OwVCL)=I+III+;______~::'^^^^`````^^^'~"1LCCCtVVw2"_)tG44WNW%####%EOB@@%%%Wt^                             . .......................................................
__________~~~~~~~~::~:::~:::::''''^''^^^^^^^^```^````````````````^_G%%%@#M$M$##@@@@MMM#$$M%WBDOwVtL)=I+;++;"__~__~~~_~~~~:::~:~~_"+I1c)TTTLLLCL";+"_1LOOwZ2LtwDBBB%@%%%W=.                             .........................................................
_________~~~_~~~~~~::::::::::'''''''^^^^^^^^^```^````````````````^;D%%%@M#MM$M@##@%MMMMMM@%B4DOw2VL)=I;;;;"""_~~_~~~_~:~__~~__~_";+I1=c)))c))T)_`"_+tVc__"_''^'_IwN@%%NW=.                             ...............................................`.........
__________~~~~~~~~::::::::'':'''''^''^^^^^^^^``^^```^````````````^"O%%%%@#M$$$##@#@%MM##@%WB4GOP2VCTcI+;"""""__~_~~~~~:~________";+11I1111=cc=+^"_+tC"^^```^^`...._CW%NB+.                             ................................................`........
__________~~~~~~~~::~::::::':'''''^^^^^^^^^^^^^^^```^````````````^"G%%%%@#@M$M####M@@%##@NBDDOPZ2VCTcI;"______~~_~~~~~~~~~~____";+III++IIII=II1_"L=^.`.`..```^'^`..`'IVO1.                            ..........................................................
_________~~~~~~~~~::::::::'':'''''^^^^^^^^^^^^``^```^`````````````_O%%%%@@@#MMM###@##@%%%%BDGGZw2VCLc1;"__~~_~~~~:::~~~~_~_~___"++++I+;;;++III;^_'^`_^....^'`.````````^^'..`.....                     ..........................................................
_________~_~~~~~~~::::::::''''''''^^^^^^^^^^^^^`^```^````````````^;E%@%@@@%@#MMM#@@#@@%%%NW4OZZw2tLL)=+"_~:~::::::::~:~___~~___"+++++;";;";+;I+`.^`.`.....`'^...`..........``......    .              ....................................................`.....
_________~_~~~_~~:~:::::::::''''''''^^^^^^^^^^^```^``````````````^+DN%%@%@@##MMM####@#@%%%%BGPOZVCCL)cI"_~::::~:'::::~___~____";;++++;;";;"_"+;....   .. .`'^.............`....  ..  .       .   .   ...................................................```.```.
__________~~~~_~~~~::::::::'''''''''^^^^^^^^^^^^`^^``^^`^````````^_w%%%@%@%@@###@@@@@#@%%NWNBDPwtCLLL=I"_~::::'''::::________";;";"";;;;;;;;"+_.``. .. . .`''............^`.        ...  .   .     .....................................................`.`.```.
__________~~~~_~~:~:::~~::::'':'''''^^^^^^^^^^^^`^^^^`^`^^''^^^^`^_P%%@@%@%@%@#@%%%%%%%%%NNWBBBEZCLTTc1"~:''':''::~___"______;;;;;"";;";;;++++I'...  .    .'~..............        ....  .   .   .  .................................................``..``.```.
_________~~~~~_~~:~::::::::'''''''''^^^^^^^^^^^^`^^^^````^^':~+)C2DN%%@%%%%%%@@%%%%%%%%%WWWWW%%WE2VCLT1"~:'''''':~__""""_";++III+++++I++II111I+....       ..:.............          .... .   .   .  ....................................................`.`.```.
_________~_~~~_~~:~:::::::::'''''''^^^^^^^^^^^^^^^^```^```^^^'^''_)t2B%%%%%%%%%%%%%%N%%%%WDGOPwtLTTccc+"~:''^'::_";+;;;";+I111=11=1111cc))ccT=c;..`. .     .^........`. .            .....       .....................................................`.```.`...
___________~~~_~~:~:::~::::'':''''''^^^^^^^^^^^^^^^``^^``^^^^:_"+====OB%%%%%%%%%%%%%WBBWN%%WDPVL)cTT)=;_::''^'~__+II;;;+II1==cTTTLLCttCCtCLLTTc:.`   .     .`......... ..            ....... .   .....................................................`.```.```.
_________~_~~~_~~:~::::::::'''''''''^^^^^^^^^^^^^^^`^`^`^^^~___"+;"";LEN%%%%%%@@@%%%NWBB44BB4GwtLttCT1"_::''':_"++;"_"""";III==cTT)cc))=1I+;"__'.          ........... .         . ............  ....................................................``.```.```.
_________~~~_~~~~:::::::::'':'^'''^'^^^^^^^^^^^^^```^```^^'__~_;":^';)PW%%%%%%%@@%%%%NBBBB4DDGwVtVtL)+_~::''::_"+"_______"";III1=III++;;__~_::'^           ..........  .          .............. .............................................................``
_________~~~_~~:~:::::::::''''''''^''^^^^^^^^^^^^```^``^'^^:_"~^``^_1LVGB%%%%%%%@@%%%NNNWBB4DOwtCTcI"_~:::':~~_;;__~:::~____;;______:':'^```....           ... .....  .          ...........................................................................`..`
_________~~~_~~~~:::::::::'':'^'''^''^^^^^^^^^^`^^``^^^^^^'~":..`^_;+I+ct2LVVEN@@@%%%NBWBDGZ2tLc1+_~:'':::':~_""_~:'^^':::~~_~:::'^^``.....    .           ...  .. .             ..........................................................................``.``
________~~~~~~~~~:::::::::'':'''''^''^^^^^^^^^`^^':__~'''':_^..`^':'^`^'':'I=ZBN%%WWB4EEOwtL)=I;__:'^^^'::'~____~:^^^'^''''':''^^^``.......   ..   .       ... .      .        .........   .........................................................`.....```.``
______~__~~~_~~:~::::::::::'''^'''^''^^^^^^^^`^'`'_"+"_~:~~^...``^^.......^:I2ZG4EOP2ZVtC)I+;"__:''^^^^^'::~_~~~:'^^''^''^^^^^^^^^```..........`.          ...                 ..             ......................................................`.....```.``
________~~~~~~~~~:::::::::'':'''''^^'^^^^^`.... ...`^:__:''`...```........^^I=)Lc=cc)=1I+"___~:''^^^^''^^''':::':'^^''^^^^^^^^^^^``^`..........``  .        ...                .                 .....................................................`.`.```.``
_________~~~~~~~~::::::::'''''^'''^^'^^^^`....  .....``'''`.....`...   . ..`_"""__;1+_~~~::::'''^^^^^^^^^'':::::''^'''^^^^^^^^^^^``^``````.``.`^^  .        ...                                   .....................................................``.``````
_______~_~~~~~~~~:::::::::'::'^'''^^'^^^^`.............`^^.........      ..'"______"_:'::'''''''^^^^^^^^^^'':''''''^^^^^^^^^'^^^^``^```^`^^^``^''.           ..                                   ......................................................`.``````
_______~~~_~~~_~~~~:::~:::::':''^''''^^^^`.............^'^`........      .._"____~__::':':::''''^^^^^''^^''::''''''^^^^^^^^^^^^^^^^^`^^^^^^^^^^'::.      .   ..                      .            ................................................`.`.`.```.````
________~~~~~~_~~~~:::::':::''''''''^^^^`...............`..........     .^.;"""__~_:::::':::''''''''^'''^'^'''''''''^^^^^^'^^''^^'^^^'^''''''''':_. .        ..                     ..             .............................................`...```.````````
_________~~~~~_~~~~:::~:::::':'''''''^^^``.........................     ..`++";__~_~:~::::::':::''''''':''::'':::::'^'''''''^^^^''''::'''''''''':~`          ..                     .              .............................................``...``.````````
________~~~~~~_~~:~:::::::::''''^'''^^^^................  .........     ..;I"""____~:::::~~:::::'':'':::::::::~~:::::::''::''''''::'::'''''':'::::' .         .                   ..                ..........................................`..`..````````````
________~~_~~~_~~:~::~~:::::''''''''^^^........  ......   .......      ..`I+"""____~:~~~~~~~~:::':::::~~~~~:~:~~~:~:::~:::::'::''::'''''':'':''''::...        .                  .                   ............................................``.````````````
________~~_~~~_~~:~:::::::::''''''''^^`......     ..  .   ......        .^+"__"_"__~:~__~~_~~~~:'':::~~:~:~:~~~:~:~~~:~:::~::''''''''''''''':''''::.     .                      .               .    .........................................`.```.````````````
________~~~~~~_~~:~:::~::::::'''''''^`....... .   ..      ...... ..   ..._"_"_"_____~~_~~__~::::::~:::~::~~:::~~::~~::~:::'''''^^^'^'''''':''''':::^                           .                      .......................................`..`.`.````````````
_________~~~_~~~~~::::::::::::''''^'^........     ...      .....  .    ..;__"___"_~~~~~~~~:::''':::::::'::::::::~:::~::::'^'''^^^^^^'^'''':''':::':^                           .              .       ..............................................`.``````````
_________~~~_~~~~~::::::~::':'''''^^`....         ...      .....  .    ..___"____~::~:::::'''''':''''^'''''':::':''':''''^^^^^^^^^^''^''''':'''::':^                                                   .........................................`.``````````````
_________~~~_~~~_~::::::~:':::'''''`...           ...       ...         :_____~__:::::''''^^'^^^'^^^^^^^^^^^'''':''^^^^^^```^^^^^^^'''''''::'''':'''.                      .               .          ........................................``...`.```````````
__________~~~~~~_~::::::~:::::'''''`...           ...       ...  .     `__~___~~~::::'^^^^^^^^`^^^`^^^`^^^^^'^^^'^^^^`.`^```^^^^^^^^^'':''':''::''''.                      .             .            .....................................`...``..`````````````
_________~~~~~~~_~::~:::~:::::'''''...            ...       .    .     `______~~::':''^^^^``^`````.`````````^`^^^^````.`````^^^^'^^''''''''''''::''^.                                  ..             ......................................`..`````````````````
__________~~~~~~_~~:~:::~:::::':'^^...           ....                  ^_____~~::''''^^^^^````.```.```.``````^``^`````.`````^^^^'^^''''''^''''::'^^^.                                 ..             .....................................`.`..````````````````^
___________~_~~~~~~:~:::~:::::':'^^...           ...`               . .:~_~~_~~:''^'^^^^^```^`..```^``.`.`.````^^`````.````^^^^^'^^^^^'''^'''''''^^^`                  .           . .               ......................................`..``````````````````
_____________~~~_~~::::::::::'':'^`....           .``                 .:__~__~::''^^^^``^`````````.```.`.`.`````^`.`^````^^^^^^^'''''''''^'''''^^^^^`.                ..       .   .                 .....................................`...`````````````````^
____________~~_~~~~~::::::::':::''^....           ..`.                ^_____~~~:'''^^^^```````^`.```````.`````^```````^``^^^^^'^'::''::''''''''^^^^``.                .      ......                 ....................................```.`````````````````^`^
________________~~_~::~:::~:::::^^`......          .`.               .:_~~~~~::::'^^^^^^^`````^```````````````````^```^^^^^^^^''':'''''^^'''''^^^^^`.`               .      ......                  ....................................```.`````````````````^^^
____________~~_~~~_~~:~~::~:::::^'`.......         ...               `_~~~~:::::''^^^^^```^```^``^^`````````.`^```^^^^^^^^^^^'''''''''^^^^^^^^^^^```...             .     .....                    ...................................`.```.`````````````````^``
____________~~__~~~~~:~~::~::::'^`......... .       .                `_~_~~:'::''^^^^^^^``^```^``^^`.```.`^``^^``^^^^`^^^^^^^'^^^^^^^^^^^^^^```````....                  .....                     . ................................``.```.`````````````^^`^^`^
_______________~~~_~~~~::::::::^``.............  .. .               .:_~~~~:'''^^^^^^`````^``````^``.``..`````^`^^^^^^^^^^^^^^^'^^^^^^^``^````````.....               ......                          ..............................``..`````````````````^`^`^^^
__"_________~~_~_~_~~~~::::::::^......... ..`...  . .              .`~:::':'''^^^^^^`````````````^``.`...`.``^^^^^^``^^^^^^^^^^^^^^^^^^``^`.```.........             .....                        .  ............................``.````````````````````^^``^^^^
_______________~_~_~~~~:::::::^..........   ..`.. ...             . ^:::''''^^^^`^^`````.`^```.``^``.`...`.```^^^^^^``^^^^^^^^^^^^^`^`````..............        .  ...                           ..   ..........................```.``..`````````````````^^^^^^`
"____________~~~_~~~~::::::::'`..........    ..`.  ..              .::''''^^^^`^^`````.```````.```.`....``..```^^^^^^``^^^^^^^^^^^^^`````............ ...          ..                            .     ...............................```..````````````^``^^```^
_______________~_~~~_~::::::~^............     .:` ...             `::':'^^''^`^^```.`..``.```..``...`.```.```^^^^^`^``^^^^^^^^^^``^````.............  ..     .   ..                             .       .........................```..``.`````````````^```^``^^
______________~~_~~~_~~::::::`.........         .`...'.            ':'^^^^^^^^`^^````..```.```.``..`.....`..``^^^^^^^`^^^^^^^^^^^``^````.............  ...    .  ..                             .       .``.................`..`..`.```````````````^```^```^```^
_____________~~~_~~~_~~::::::`.........            ..`.            ':'^^'^^^^^````.```.`````^`.```.........```^^^^^^^^^^^^^^^^^^^```````.........     ....                                              .'`........................``.`````````````````^```^`^^^
_____________~_~_~~~_~~::::::`......... .   .        `^.        . .':'^^^^^^^^``^`.`.`.``````````..........````^^^^^^^^^'^^^^^^`^````........  .        ...                                            .^^`................`....`..````````````````^```^```^^^^^
______________~~_~~~_~~::::::^............  .         ...       ..^:''^^^^'^^```^```^```^^```````...........`^^^^^^^''^^^^'^^^^^^``^`..`....          .....  . . "` .                                  .'``.......................`````````````````^```^``^^^^^^
"______________~_~~~_~~:~::::^.................        ..       ..^:''^^^^^^^^`^^````^``^^`^``.`...........`^^^^^^''''^''''^^^^^`````.......   .       ...`.    ^. ..                                  ^^.........................`````````````````^```^`^^^^^^^
"________________~~~_~~~~::::`...................        .       .':''^'^^^^^^`^^^^^^^`^^^`^``.............``^'''''':''''''^^^^^^^```.......            ..`` .  . ..                          .. .    ........................`````````````````^```^```^^^^^^^^^
_""______________~_~~~_~~~:::`......................     ..      .::''''^''^^^^^^^^^^^^^`^^^```............``'':':::''''''''^^^^^^`^``.....             ..`^..  . .                          .....    ...............``.``..`...```````````````^`^`^^^^^^^^^^^^^
"""________________~_~_~~::::^... ...................     .      `~:':::''^'^^^^''''^^^^^^^````..`.........`^'~:::~:::::'':'^'^^^^```.........        .  ..^^. .              .              .  ...  ...............`.`.``..`````````````````^`^`^``^^^^^^^^^^^^
_"""__"____________~~~_~~:~:~^... ..    ...............    .    .`~~::::':::'':''^'^^^'^`^^`.```..........`^':_~~:~~~:::':''^^^^^^^```........       .....`^'....                           ...:.  ......`..........``..```.````````````````^^```^```^^^^^^^^^^^
_"""_____________~_~~__~~:~:::.......                ........    `____~~:::''':'''''^^'^`^^`.```..........`^'~___~~~~~~:::'''^^^^^^``..........      ......^_'`... .                        ..^+_. ......`..........```.```````````````````````^`^`^^^^^^^^^^^^^
__""__""___________~~~_~~~::::^.... ...                 ......  .';"___~~~::'':''':'^^^^^^^`````.........`^':______~~~~:':''''^^^^^````........ ... ......`^"_........ .                    . '_+_ ..   ..........`.``..```````````````````^`^^^`^^^^^^^^^^^^^^^
_"""_______________~~~_~~~~:~:'..... ..           ....     ..`...:+;"___~~~:'':''':''^^^`^^`.```.........`^'~_"_____~~_~:::''''^^^^^``...................``:_..  . .            .            .':_+^ ..   ........``.```.````````````````^^``^^```^^^^^^^^^^^^^^^
;""""""____________~___~_~~:~::...... ..            .....  ..^'..~I;"___~::::::''''''^^^^^^^````........``^:_""____~~~_~:::'''^^^^^```..``...............^^:`     ..^_`     .^':.    ....  .^^^':~":....  ..........```.`````````````````^^``^^`^^^^^^^^^^^^^''^
;"_""___"__________~_~~~_~~:~~:`.....  ..            ...`.  .`^.._++;____:::::''''^'''^^^^``^`.`........`^^:_""____~_~~::::'''^^^^^^`.```................`'~^.+_'':':~`    `^^^^.   .^^^^.`^^^^'':_____'.   .......``..````````````````^```^```^`^^^^^^^^^^^^^''
;"__""__"__________~_~~~_~~~~::^....... .              ..`. .....;++;__~_~::::'''''''^^^^^````..........``'~"""____~_~::::'':'^^^^^^`.```..............``^':__++_:^^`.``...........``.```.````^^^'~"""_'............```````````````````^```````^^^^^^^^^^^^'^^''
;"__""_____________~_~~~_~~~~:::`...`.. .               ..'`.....++;;____:'::''''''''^^^^^```..`.......``^'_+;"""__~_~::::'':'^^^^^^`````.`............`^^'~+Vc"~^^^.......................`.`^^^':__"_'`......``..````````````````^```^```^`^^^^^^^^^^^^^^^^^''
;"_";__""___"_________~~_~~~_~::'.  ... ...             ...`'`...;;;;____::'''^'''^^^^^^^```.`.`.`...`.``^'"++"___~~~:::::''''^^^^^^^````.`...........`^`^'_ItI_:^^`.........................``^^':____:'``....``..````````````````^```^``^^`^^^^^^^^^^'^^^'^^''
"""""___"__________~__~~~~~~~~::~^.   .....`.          .....`~:.'+;""__~_:::''''''^^^'^^^^````.``...```^^^~;I+"___~~~:::::'''^^^^^^^`````.............`^^^:_1L+_:^^``......................`.`^^'':__"""^......``.`````````````````^```^^``^`^^^^^^^^^^'^^^''^''
"""";"_""_____________~~_~~~_~~:~:.    .....'`.       ........"_;;;""__~~:::'^^'''^^^^^^^^``.`.``..``^`^':_+I;___~~~::':::''^^^^^`^^```^``.``......`..`^^^:_cT"_:^^^`......................```^^'':__"_``..``..``.`````````````^```^```^^^^^^^^^^^^^^^^''^'''^''
;""";"_"____"__________~_~~~_~~~~:^.   ...  .. .. . .........`.~+;"_"_~~~::::'''^^^^^^^^^````......`^^^^:~_II;___~~:::''''''^^^^^^^^^``^``.``..``..`..`^^^~"))_~:^```.....................```^^'':~___'.....`..````````````````^```^``^^^^^^^^^^^^^^^^^''^'''^''
;""""""";__""__________~_~~~~~~~~:'^. ...     ........  .^:_~.^+;;____~~~:::''^^^^^^^``^^`.``......``^^':~"I+"___~::''''''^^^^^`^`^^``````.``..``.....`^^'_+TI_:'^^`.....................``^`^^''~__"_^....`..`````````````````^^``^``^^^^^^^^^^^^^^^^'''^'''^''
"";""";"""_"_______________~~~_~~:~'^`...     .....    `_I=c':++;;""___~~:~:'^''^^^^^^^`````.......``^^':_+1+"___~::'''''''^^^^^^^^^`^````..```````.```^^'_+LI_:'^^.....................````^^'':___""^.`````````````````````^`^^^^^^^^^^^^^^^^^^^^^^''''''^''''
"";""""";";"_""____________~~~_~~~~'''^..     ...`^`^:_"___:."+I;;""___~~::'^^^^^^^^``^`.```.......``^'::_I1;"_~~~:''''^''^^^^^^^^^^^^^``````````^`````^^'_1L+~'^^`..................`..````^^'':___"_`..````````````````````^`^`^`^^^^^^^^^^^^^^^^^^''''''':'''
";;""""""";"________________~~_~~:^......''.  .;I+;"_~::'':.`;1+""""___::::'^^^^^^^`````.```.......``^':~"=I"__~:::'^^'^^'^^^^^`^^^^^^^^^^^``````````^^^^:_=T_~'^``..................`...``^^''::___"~`.`````````````````^```^^^^^^^^^^^^^^^^^^^^'^^'''''''':::'
";;""""""";"________________~~_~~^.    ......_="___:''^^^:''"II;;""___~~::'^^^^^^`^`.``..``........``^:~_;=I"__~::'''^^^^^^^^^^``^^^''^^^^^^^^^``````^`^':_)c_:^^`....................`````^^'::~___"'```````````````````^`^`^^^^^^^^^^^^^^^^^'^^''^''''''':'::'
"""""";"""""""_______________~_~~:..   ...^_1I;__~::'^'''~_'+1++;;;___~~''^^^^^````.................`^'~_+cI"_~:::''^^^^^^^`^`^^`^^''~~__"_~~:'^^^```^^^^:"L=~'^``...................``^^^^^'':~_"___^```````````````^```^^`^^^`^^^^^^^^^^^^^''^'''^''''''''::::
";;""";"""""""_________________~_~'.^__;+T)=I+;__~::'''^':`~=I1+;;"____:''^^^```.``.................`^:~_1=+__~:'''^^^^^^^^```^^^^':_";"_;;+__~^^^```^^^^:"CI~'^``..................``^^^''':~~__"";_^``````````````^^```^^^^^^^^^^^^^^^^^^^^''^''''''''':''::::
+;;""";""";""""_________________~:^`._I))))cI++"___:'^:''.~=11+I;""__~_:'^^`````....................`^:~_=T+_~:''''^^`^^^^^``^^^'~_+;+;";;;;+++":^^```^^':+C;:^```...............```^^^'':::~_____";~````````````````^``^^^^^^^^^^^^^^^^^''^'^''''''''''':''::::
;;+;"";;";;"""""_""______________:^``_1)L)Tc=I+;___::'':`.+=1I1I+++____:^^^^`.......................`^:_+=)+__:'^^^^``^^``````^'~_;I+;+;;""+";;;_'^^`^^^':+C;:^`.`...........````^^^^':::~___""_""";:```````````^^``^^``^^^^^^^^^^^^^^^^''^^'''''''''':'::':::::
++;;+""""""";"_"______________~~_~:^^"I)LTTc=I;;__~:~:^'..;=11IIII;"__~'^^^``......... ......   ....`^:_Ic=+_~''^^^`````^`.```^'~_;+;;;;;;";"_";_'^^``^^^'IL"'^^.............``^`^^''':~___"""";__";:`````````````^^``^^```^`^^^^^^^^^^''^^''^''''''''':'''::'::
++;;+;"";;"";"_"_______________~~~~~:"c)CL))cI;""_::_':`^"===cc))c=+"_~'^^``...... ..       .   ....`':"1c=+_~''^`````..``..``^:__""""+++"+"___""~'^``^^''1L_'^`.......`.```^^^''::___"+++++"_~_;_""^``````````^```^``^^^^^^^^^^^^^^^^^''^'''^'''^':''':''::::::
+++++;"";"""""""_______________~__~~_:_;CLT))I;"__~~::'. _c)LCCCT)=II+_'^``......   .       .   . ..`'~;=c1+_~'^^```....`...``^:___"""";++"+"____~'^^`^^':=c_^^^`..``.`^^^^''':~_;;IIIII;+_^`^^^::^^```````^```^```^```^`^^^^^^^^^^^'^'''^'''^''''':''':''':::::
++;++;;";""";"""""_______________~~~_~~"CCLTc1+;"__~~:~:.;TCVCL)T=1=1;_:^`.... ...              . ..^'~+==+;_~^^^````.......``^~______"I11I+__""__:^^^^^'_==~'^^`````^^'::~__;;+II+;++;"_~:`   .`..````````^^``^```^^^^^^^^^^^^^^^^''^'''^'''^''''':''':::::::::
+;;++;"";"_"""_"____"______________~__~_TtT))1I;"_~~:::_"Tt2VCL))1I1+_~'^....                    . .^:_Ic=++_~'^^````........`^~~_____1))))I+"____:^`^^':_c1:'````^^':_"""___~__~::::::~'``^. ..^:_^```^``````^^``^^^^^^^^^^^^^^^^^''^'''^''''':''::''::::'~::::
+;;++;";;;""""""____"________________~~_TCL))=+;"_~::::_ct22VLTTc1++;_~'^...                    .. .^:_+cI";_:^^^``.`.........^:~~:~~_1;""=1"_____~:^^^':_)+~^^^^^':___::~~::''^^`````^^^```^^':_+_````^```^^``^^`^^^^^^^^^^^^^^'^'''^''''''''':''':'':~:::~::::
++;++;";;"_";""";"__"_________________~_TtLT)=I;__~~::_"Cw2VtCLc1=+__~:^`...                    ....^~_1)I_;;~^^^``.......  ..^::''^'~;;""+I_~~~~~:^`^':_;T+~^^'::_"_'^^^`^'^```......```````^~;++:^```^```^^^^^^^^^^^^^^^^^^^^''^'''^':'''''''::':::::~:::::::~
+++++++;;;;"";""""""__"__""_____________)ttTc=1;___~:~_;CwwVtLTc=1+__~:^...                     ...`^~;1c+_;;~'^^```..........^''''^'~;+_+I__~~~~_~^`^''_IL+_':'__"_~'^^`...^`.`.....`.`````'~;+++:^`^^`^^^^^^^^^^^^^^^^^^^^^''^'''''''''::'':'::::::::::~:::~:~
++++++++;;;"""""";;"_"__________________)tLL)=1;___~:__IwZw2CLL)I;"_~~:^`..                      ..`'_+=)+_""_''```.....  .....^'^^`^^'~__~~::'':~'``^'~"TL+_~__;_:^^^`... ..``..````^^^':~_;++;++'^^`^`^^^^^^^^^^^^^^^^^^^''''^'''''''''''''::::::::~:::~:::~~~
+++++++++;;;"";;"";"_""___"___"_________cVCLTc1;_____"_=Zww2wwtc+"_~:'^^..                      ..`^:_+=)"__;_~'^```.... . ....^^^^``````^^''^^'::^``^:~+VC+"_;_~^``...... ..``^^''''~"+;;;;;;+;I_^^^`^^^^^^^^^^^^^^^^^^^^^^'''''''''''''::''::::::::~:::~:::~~~
+++++++++++;";;""";""";"_""_____________=tCL)c=I"______)ZZ2ZtLL=;_~:'^^`..                     ...`^~"I)c_~_""~'^^^.....      .`^^^^``....``^^^'':``^'~;cPC=I;~'^``..........^'_;"_;+1++;;"""++I+'`^`^^^^^^^^^^^^^^^^^^^^'''''''''''':':'::':::::~:~:~:::::::~~~
++++++++++++""";"";;"";"________________=tCTcc1I+"_____)P2PwTI++;~~'^^^`..                     ...^^~_+)I_~_"+_~'^``....  .    .^^^^``.....``^'^'^``^:_1wEL+_'^```.........`^^:;=))1I;"""__""++1"^``^^^^^^^^^^^^^^^^^^'^'''''''''''''::::::':::::~:::::::~::~_~_
+I++++++++++";;""";;;;;"""_"____________=tCT)c1I;"____")w22wL1I"~~:^^``...                    ...`^'~_=L;_~__++_:'^`...  .      ..^^`^`..``^^^^^^^`^:_IV21_~'^````........``^~"1T)1I;;______";+=_^^`^^^^^^^^^^^^^^^^^'^^''''''''':':'::':::::::::~:::::::~~~~_~~
III+++++++++;";""";;";;"_""__""_________1tC)c=1I;"____")ZVttC)1_~~'^`....                     ...`^'~;=L"___"+I"~:^`.....        ...`^^````^^^^``'':_ItL"_'^^^^^``...`...``^^^:~_+I+;"______"+II:^^^^^^^^^^^^^^^^''^'''^'''^''''':'':::::::::~:::~::::::~~~~~_~~
++II++++++++++;"";;;"";"_"_"_""_________+CtL)=1++"__~__=wVLc1+;__:^^```.                     ....`^:_ILT"___;I1I_~'^`.....          .^^``.`^^^^^:~_;)wc_:^^^^^`^^``..`...`..`^^^:~"++;"___";++1"^^^^^^^^^^^^^^^^^''^'''^'''^'''':::::::':::::~:::~::::::~~~~~_~~
II++++++++;;++;";""";"""""__""__""______+LL))1I++;_____I2VT=I+"_~:^``...                     ...`^^~"IL)"___;III+_'^``...  .       .......`^^^':~_;ctL":'^':^^`^```...........`^''_;++"""_;+++1_^^^^^^^^^^^^^^^'^^^''^'''^'''''::':::':::::~:::::::::::~~:~~~~~_
I++II++++++;++;;;"""""""""_""__""_______;LLT)1I+;"_____;tVT)1+___:^^`..                      ..`^^'~;cVc"_";+II11;~:^^`......         ....^'~__+1ctT+_~~~::'^^```...............^^^:_"+1+++II1I'^^^^^^^^^^^^^^^''^'''^'''^''''':'':::':::::::::::::~::~~~~~_~~~_
II+II++++++++++;;"""""""""_"""__________;LCTc=1++;_____;TV))=+___:'^^`..                    ....^':_1LtI;""++I1=cc+_:^^`......        .`:~"+1c))cI++;+++"_~:'^`^`....  .   .......`^^:_;II1==c"^^^^^^^^^^^'^^^'''^''''''''':''':'':::::::::~:::~::~~~:~~~~~_~_~_
+I++II+II+;+++;;+;""""""""_"""_"""_______)LT)c1II;_____"ICtLc+___::''`.                     ...`^:_+)2LI;"";+I1=)T)1_:^^```.......```^~_Icc=I;"_~:~~~~~___~~:'^^^`......  ...........``'~_+=))~^^^^^^^^^^^'''^'''^'''^'''':::'::'::::::::::::::~:~~~~~~~~~~_~_~_
II+III++++++++;++;;;;"""""_"""_""________cLLTc1II;""____+)tLc1+"__~::`.                    ..`^'~_+=tZcI+;;+I11=TLLL)+_~:'^^^^^^''~_;I11;__~~::'^^^^^^'':~~:''''^```..........`^`......^^^:_1I~^^^^^^^^^^^'''^'''^''''':''':'':::':::::::::::::~~~~_~~~_~~~_~___
II+III+II++++++++;;";""""""";"_""___"____=CLTc11+;_____"+ITLL)=I__~:^`.                  ....`'~"I)tOV=II++I1=c)TLLtVL)1+"____"+==c=;___~:':^^^^^```...``^^^^^^^^^^^`.......```^``.`...````'_I1"'^^^'^''^^'''^'''^''''':''':'::::::::::~::::::~~~~~_~~~_~~~_~___
1IIIII+II+++++++++;;;""""""""""";"_""___"1CLT=1I1++"""_";+=))=11+_~:^`..                ...`^'_;1TtOEC=1I11=c=)TtLt22w22VCLCLTc1;____:~~'^'^````^`.....`..........``.........``^^``^^^`^^^^^^~+=I~'''^'''^''^''''^':''::':'::::::::::::~~~:~~~~_~~~_~~~_~~~_____
II1IIIII++++++++++++;;;;;;;;"";"""""""___ItC)c=11I+""";"";1=c=1I+_~:'^..               ....`^~"IctZEPLc=1==ccTLLCCV22wPPZwVt)=+"___~~~::''^^```````..................`.......```^^``^^'^^^``^'_II+_^'''''''''''''':':::::::::~:::::::~::~~~~~_~~__~~__~_________
11=IIIIIIII+++++;+++;++;"";;"";""";"""_""+CLTc==I+I+"____;I===1I;_~:'^`...             ...^'~;cLVOB4tL)cc))T)TTLtVV2wZwVc+""____~~~::::'^^^`.`..```..................`.......``````^^'```````'_";+I":''''''''''':':::::':::::~~::::~~~:~~~~~~_~~__~~__~_________
I1==IIIIIIII++++++++++++;;"""";"";;"_"___;LCT)c1++I+"";"_"+1cc1I"__~:^^.....          ..`'~"1TtPEBWZCLTT)TLTTLCCtCLcI+;;_~_~~~::~::''^^^`^`...........  ........ .. .................```^^``':~"__"++_:^'''''::':::::::::~:~~~~~~~:~~~~~~_~~~_~~~_______________
I==IIIII+IIII+++++++++++;;;;";;;;";;""_""")CTT)=III++;;__"+I=TcI"__~:'^``..... .  ....^':"1TVPEBWNEwtCCtTLLT)==I+;;"___~:::'':''^^^^^^`````.... ..       .. .....     ...........`.```.`^''::_""~__";+~''''::::'::::::::~~:::~~~~~~~~_~~~_~~~_~~________________
11=111IIIIII++I+++++++++;;+"";;""";;";"""_1CLTc=1I++;;"_;I1=c)L);+"_~:'^^``......`^^':_I)2PDBBBB4OwtT)Tc=1I++;;____~~:::'''^^^'^`^```^`.......               ....    .. .........``.```^^:~~"1+_~~__"+_':::':::':::::~:::~::~~~~~~~~~_~~~___~_~_________________
11=1111IIIIII+I++++++++++++;;";;"";""""""";LLT)=1I+;;;;IcTCtL)TCC1I;__~:''^^^^^^^'~_=tZPZVTc1I11II1I+++;""_____~::::''''^^^^^^^^^^````......... .            .. ....... ... .....`....`^^'~";)=______"_':::::::::::::::::~:::~~~~_~~~_~~~__~____________________
111111==I1IIIIIIII+++++++++;+;+;;";"";;""";)LLTc=II++"+=cI+=VVTCwPV=I;"_~:::::_"=CVVLcIIIII+++++++++;"____~~~::'''^^^^^^^^^^``^`.`............           .   .      ...........`.....``^^^:~Ic2C1"__~_~::::::::::::::~:::~::~~~~__~~~_~~~_~~____________________
11=111==I1IIIIII+II++++++++;+;+;;";"";;""""cCTTc=11II+11_~~_=22t2PD4Ot)===cLC22C)1+++;++";;;";""_"____~:':::'''^^^^^^^^^``````^`.............            .   .    .  .......`...`...`.`^'~~~+=LO2TI__~::::::::::~~:::~:::~:~~~~~~_~~~_~~~_~___________________""
1=11=111=IIIII+II++;++;++;;;++;;;""";""";""ItLT)==III+II_:^:+)w2wPEBBBOPZww2VL=I++;;+"""___"______~~~~::''^^'^^^^^``^```^``.`.`.............                   .   .   ....`..........`^`^'_"=)T=+"_:::::::::':::::~:::~~:~~~~~_~~~~~~~~~~~_~______________""___
=111=111=1I1II+III+++;++++++++++++;";""";""+CCT)c1I1II=;^..^"+twVZPPwtL))1+;;;;++"__"_~_~_~_~~~~~::::'^^'^^^^^^`^``````.`.`.`..............                            .. ............```^^^~+=1+~:::':::::::':::::~:~~~~~~_~~~_~~~_~~~____________________"____
=====111=11IIIIIII+I++++++++++;;;;;;;""";""+LtLTT=111Icc+;;;1+)ZVVL)=II++";"""________~~~~:::::::'''^^^^^^``^````````.......`.....````.`....                    . .     ...........`..```^'~_"++II;::::~:::~:::~:~~~:~~~~~~_~~~_~~___~____________________"""_";
==1==111=111=IIIII+II+++++;+++;+++";;""";""")tLTLc1I1=C)+;__"+cwV)=I++;;"________~:~_:::''''''''^^^^^^^`^`````...``.....`.........````........ .       .                   .  .......`^^':_____";+II~':::::~:::~:~:~~~~~~~~_~~~_~~_____________________"__""__""
=====11===11=1II=1III+++++++++;+++;;+;"";";;1tLTTc1=1cL)1+;;"+cVT=I++;""__~___~~~:':::''''^'^^^^^^^^^^^```.``.....`................``..........      ..........           ....... ...`^'______~__;++_::::::~:::~~~~_~~~_~~~~~~_________________________""_";""";
cc====1==111=1IIIIIIII++II+++++++++++;;";"""ICLTT)==1cT=1;___"cC=++;;"____~__~:~::::''^^^^^^^^^^^`^```````.``.......................`.`........    .`.``........          .......  ...^:_=LI_~:~__;;_~:::::~:~~~~~~_~~~_~~~_~~_________________________"""";""";
=====c====111111=1III+IIIIII++++++;;++;;;""";LVCL)===)cI+_~:_")T1;""______~~~:::::':''^^^^^^^``^^`````.``...`......................```.............`^^^^^```.....            .........`^_IcVc_~:~:_"_::~::~_~~~_~~~_~~~_~~~_~__________________________"""""""";
=ccc========11=1I==II+I1IIII+++++++;+++;;";;"TVCTT)c=TTI;_~:~"L)I;"________~:::::::'''^^^^^^^^^```^````.`.................`........````..`..```..`^^'^^`^^`....  .          ......`.....:I+)V=_:~~~__~~~~~~~~_~~~_~~~_~~~__________________"____""__";"_";""";";
=cccccccc==111=1111IIIIIIIIIII+++++++++;;++;"cVtLTT))LT+_~':~"T=;"_________:':::''''^^^'^^^^^^^````````..`.`..`...................```````^^`^':"1CLc=;:^^^....                .......``^_+I"=V1_~~___~~~~~~~~_~~~_~~~__~~_________________"__""_""";";;"""""";";
=ccc=cccccc==1=11==IIIIIIIII+I+++++++++++;+++1VtCLTLTLLI_~:':_cI"";_~__~~~~~::''''''^^^^^^^``````.`````..............................``^^^:;TV22VttCtCtT;^....                   ...`'~_"";"+I_~~~~~~_~~~__~~~~~~_~~~___________________""""""""""""";""";""""";
=)c)cccc========1==111=1IIII+III++++++++++++;+LVCCLLLCCI_:'''~1I""__~~~~:~~:::'''''^^^^^^^````^``````.`.`.........`................`^^':IVZ2CLT))))cccc=))+'... .... .           ...'_"____;+;"~~~~~~~~~~_~~~_~~~_~~__~______________"__""""""";;;""""""";""++++
=)))cccc=ccc=====1==1==1IIIIIIIIIII+++++++++++)V2tLLLtLI_:'''~I1""___~~___~:'::'^'''^^^^^`^^````.```..``..``.``...``...........```^^_ItwC)c1=II1II+;++";;;Ic1_`............         :=":~~_"";"~~_~~~_~~~__~~_~~__~________________"_____""_";";";""""""";;+;;;+
=)T)cccc=cc======1==1==11I11II1IIIII++++++++++122VtCt2CI_~'::~+="______~~~~~~~:::'''^^^^^`^```^`````````.``.```````.``^`.`^^^^^':_=LC)I"""""""_______________+I;_'`..````....       ~))I_~___"~~__~~~~~~~__~~____________________"___"__";"_";";";"";"";;;;;++++
cTT)c)cc=cccccc======1=1111=1111IIII+III+++++=wPw2tttVL+_~:~__+1;"______~~~~::::::''''^^^^^^`^^```````^``````````.``^`^^^^:::_ctL)I"__~::~~:~~~~~~~~~~::~~:::::~___~:::''^^`.......^++___~~~__~~~~~~~_~~~___~____________________"______";"_";"""";"";;;++++++++
c)TT))T)cccccccc========111II11IIIIIIIII++II1VOEPw2VVtc+_~:::_+cI;"________~~:::''::''^^^'^^^^^^``^```^^^`^```^^^^^^^:~~_"ILC)+___~:::'''''^'''''''''''''''^^^^''::'::~_""~'^^^^^'_"";_~~_~~~~~~~_~~~_~~~_________________________""";""";""";""";;;;+;;;+++++++
))c)T)))cc=ccc========11=1III1IIII+III++I++ILwPEEPw2VL=;_:'':_"c1"________~:~:':'''''^^^^^^^^^^^^^^^^`^^^`^```^^''':~~_"1LtT+____~:'''''^^^^^^^^^^^'^^''^^^^^^^^^^^^'':__""~'^''':_"_"_~~~~_~~~_~~~_~~~_~~_________________"_______"__";""";"""""";+;;+++;++++++
))))T)))cccccc=cc====11==11111I1IIIIII++I++LwZOBBGPwVTI_~'^''~_c)+"_"_____~~::::::':::^^'^^^^^^^^^^^^^^^^^^^^^^''~_;=LVVc;""__~::'^^^^^^^^`^^^^^^^^^^^^'^^^^^`^^^^^^^':_____""~'::~_""__~~~~~~~~~~~_~~~__~_________________"______";""""""";"""""";+;;+++;++++++
)T))))))))cc)==ccc====1==111=1II1IIIIIII1ICwwODB%BGOV)+_:'`^':_+L1"";_____~_~:::::::::'':'''''^''''''''''''::~__+cVwC1+""___~:'''^^^^^^^^^`^^^^^^^^^^^^'^^^^^^^^^^^^^^:~__~~_"1=~'~_"_~_~~~~~~~_~~~_~___________________________"_";""";"""+"""";;++;;+++++++++I
T)))T)))))cccc=ccc========1==1111IIIIIIIITw22wOB%%EVL)+_'^`^:~_;LT++;""______~::_~~~~:~_~~:~~:::~~:::::~~__"+cC2wTI+++"___~::'''^^^^^^`^```^^^`^`^^^^^^^^^^^^^^^^^^^^':~~~~~~_;=1";+;__~~~~_~~~_~~________________________"__""""_""""";;"";";;+;+++++++++++I++I
)T))T)))))c))ccccc=c======11=11111II1III=V2w2wZPEwcLL1"~'^^^':_;)L=1+;;;"";"_______"___"_________""";"";I1)Vwt=I+++;""_~~:':''^^^^^^```````````^`^^^^^^^^^^^^^^^^^^^'':~~_~_~_"I+;I+"_:~_~__~_~____________________"______"""""""""""""";""+;;++;;+++;++++++IIII
TTTTT))))))))ccccc=c=c==c=11=111=1I1=1II=VZZ2VCLCC2tcI_~'^^^''~"ctLc=1II1I+++;;;++;;II++I+++I+II==1=c)TtPwC=1+;;;;"__~:'''^^^^^^^``````^`````````^^^`^^^^^^^^^^^^^^^'':~~_~__~_++++"_~'^:::_~______________________"____"_""""";""";"";;;;;+++++++++++++++III+II
TTTTTT))))c)T)c)cc=ccc=cc=1c==1==111=111=CZVCCCtLtVL=+_~:'^''::_=22tLccc==========1=cc===cc))))TLCVVZGOtcI++;;"""_~~:'^^^```^`````.`.`.````````^^`^^^^^^^^^^^^^^^`^^':~~~____~"+;;"_~^^`'~''~~_________________"________""""""""""""";;+;;+++;+++++++++I++IIIIII
TLLTTTT)))))))T)c)cccccc====1=======1=111LPVLLCCLtVL=I;~:'':':~_1ZP2CLT))))c))T)))TTTTT))TTTLCCV2wZOEOC1I+++";;__~~:''^^``````````..```````````^^^^^^^^^^^^^^^^^^^^^':~~~_____""+;"_:^`.`~:`'_______________""__""___"""";""";";;;"";++;;++++++++I+++II+II++IIII
LLLLLTLT)TT)))))cccccccc=ccc=======11111I)VtCLLTCtC)1+"~:'''':~_+tDOP2tCLLLLLLCttttttCtttV222ZOOD4GV=I+I;;""___:::''^^^```^`.```````....`^``^^^^^^^^^^^^^^^^^^^^^'^^::~~~_______"_:^`.....'^`^_~___________"_""_"""_""""";;"";"";;";++++++++++++++IIIIIIIIIII=11
LLLLLTTT)T))))T))))cccccccc==c=====11111I)tCCLTTLLCTI;_:''''::~_+LDDGPw2ttttttVVV22222ZZPPOGE44EVc11+++"""__~::'^^^^````....``.`.``.``````^`^^^^^^^^^^^^^^^^'^^^^''':~~:~~~:_:..``............^_________""_""""_";"_";""";"";;;;+++;++++++++++I+III+IIII1IIII=11
LLLLLLLTLTL)))))T))ccccc==cc========11==1)ttVLLLLtC=+"_:':::^^:"=TEBDDEOPZZZZZPPPPPOOGGGEED4E2)=I++;""___~:::''^^``..``...`....`.``.````^``^^^^^^'^^^'^^^^^^^^^^^''::~~~~~~~^..  ..... ........^_____""_"""""""""""";""";;;;;++++++++++++++II+++IIIIIIIII11I1=1=
LLLLLLLLTTLT))T)))Tccccc=cc==ccc=========cLVtLCLLtLI;__::::'^`^:_1VBWWB44DDEEEDEGDDEEEED4GZL=I+_""___~~:''''^^^^```..........```..`.```^^^^^^^^^^^^^^''^^^^^^^''::~~~_~~__^.             .   ...:_____"__"""";""";"";;";";;;++++++++++++II++I+I+III+II111=111===
LCLLLLLLTTTT)TTT))T)c))c=ccc=ccc========1=T2VLCLtVTI+"_::~:'^^'";=VBWNNBBBB4DDEEDD44BNBP)c1I"____~~~:::'^^^^^`````................`````^^^^^^^^^^'^^^'^^^''''''':__~~_~:`..              .     .`___"""_""""";""";;"";;+;;+++++++++++I++IIIIIIIIII1=1=1=1=111===
LCLLLLLLLLLTTTTTT)T)))T)cc===ccccc=========L2VtttVc+""_:':~:'':"=)wWNWNNBBBBBBWWWBBBPC=I+"___~~~:::''^^^`^^````..``........`````.`````^^^^^^^^^^^''^':''':::~_~~____:^..                 .     ..:__""_""""";;"";;;;;+;;++++++++++++II++IIIIIIII11III==1===1====
LLCCCCLLLLLLTLTT))T))TTT))ccccccccccc=c====cVwttVt=I;__~~_~~::'_1LCC=B#@%W44DEDGOwL1I+;;_:::':''^^^`^^``````...........``.``.```.```^^^^^'^^^'^^'''':''':~~:~~:~~:^....                      .  .`__"";"";;;;;;;;;;;;+++++++++++II+IIII+IIIIII1I1===1=1========c
LLLLCLLLLLLLLT))T)))))))T)=ccc=cc==ccc=====cC2tV2C=++"___~~__::_1CtTV%%%%WDGPPZ2CcI";____:'''^^^^`````.```..............`..````````^^`^^^'':'^''''''':'::::::'::^`...                           .._""_";""";""";;;;+;;++++++++++I+III+IIIII1II111I1=1I1========c
CCCttCLLLTLLLLTTT)))T)))T)cc)c=ccc=ccc==c===cVVV2L1II+___~_____;I=LVW%%NBEPCL)=I+"___~~:'^``^`````.``..............``..```..``````^^^^^'^'''''::::::::__:''''^`.....                           ...:"__";""";;;";;;;+;+++++++++I+I+III+II1II1III1111=111===1=====
CCCCtCLCCLLLLLLLLT)TT)))T)c)))ccccccccccc====Lww2L111+_~_______+1))TCCC)c=+++;___~::'''^``.``..`...................````````^^^^^^^^^^'^''::::::'''::::~~~''`......                         .......^"""";""";;;;++;+++;++++++++I+I+III+11II111111111=11=====c====
inserted by FC2 system